DescentComposition from Permutation
The composition of n cut at the descent positions.
Its parts sum to n and its length is one more than Descents — another statistic readable off a map. Removed once for erroring on words with no descents; Range(1, 0) never evaluates, so the short case has to be stated.
Called as CombinatorialMap(x, "DescentComposition"). The head's page has its examples.
Live
FindStat Mp00071
descent composition
Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.
The descent composition of a permutation.
| Object | Image |
|---|---|
[1] | [1] |
[1,2] | [2] |
[2,1] | [1,1] |
[1,2,3] | [3] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00071 has the rest.